I am running a factor analysis and have a couple of questions.
I have 10 variables, all of them come from a survey, with each answer is in the scale of 1 to 7. I have calculated a correlation matrix between the 10 variables, and looked for correlations of 0.5 or higher. These made me notice of 4 groups of correlated variables, two groups of 3 variables and two groups of 2 variables.
Then I ran the factor analysis. According to the scree plot, I should take 4 factors. According to the eigenvalues, the 4th eigenvalue is 1.006, so it's slightly on the line, it is larger than 1, but not by much...In addition, after 4 factor the cumulative variance is 82%. After 3 it is only 72%.
My question is, should I choose 4 factors or 3 ? Is it OK to have a factor with only two variables that construct it ? I know that a single variable factor is something we don't want, just like we don't want a sample-specific factors. But what is the rule regarding two variables in a factor ? I looked on the net, and found one document saying the minimum is 3. I didn't see any mathematical explanation and I am not convinced. What can you recommend me ?
Thank you in advance !